For some reason, it went over my head that you can play solo on the 4-player version. You simply can chose to play differen't factions that were allies of Austria instead of controlling all of them. This is wonderful!

So which version of the full campaign do people play solo? The standard version, you can control all of the allies as Austria. Althought this is fun, it might force unrealistic use of allies. Playing the four player version, your allies have different agenda's and victory conditions, so they might not always cooperate. I found this quite fun playing as France, while not having to worry about controling the other allies. I had to hope they were doing well.

Which version do most like to play on solo and why? Which offers the better campaign?

If you are going to do this, then the natural side to pick is Austria as you are the part of the coalition that is most important and active. On the other hand an AI Russia has problems with sorting out the early moves while its relatively easy for a player.

So I'd suggest an Austro-Russian alliance and let France go AI. Probably realistic given the historical antipathy between the Austrians and the French.

But, if you want to play the Austrian side vs the AI, want to control all and still want a good game then use the harshest activation rule (ie inactive most likely means fixed for that turn). Learn to love what a bunch of 3 star generals can do to an offensive, have to revert to brute force as that is the only safe option, panic about pulling back to winter quarters in October just in case you get caught either by being inactive or an early winter.

Best way to understand why the historical war lasted Seven Years and ended in an exhausting stalemate.